How do you completely compromise a machine given a text box or badly validated input box? This is a place to talk about code issues (PHP includes, null byte injection, backticks, pipe, etc...) as well as how to properly construct an SQL injection attack.

generally, this could be anything or nothing at all. If it is part of a URL, it looks like an ordinary GET parameter which is passed to the server. This could be a product id of a shop item, the id of a forum member, a page id generated by some weird CMS ... without knowing the context, anything is possible.

From the characters used in "365b158b-a0ca-41ca-9337-2f6ed2e6e3bb" it looks like hexadecimal numbers, separated by hyphens.

this behaviour is not an indicator of a vulnerability, it could be that the script is testing the parameter for plausibility inside an if/else construct which redirects all strange or non-fitting requests to the start page instead of showing an error message or doing nothing at all.

From the presence or absence of error messages and redirects alone we cannot conclude that there is some SQL injection vulnerability, as long as we know nothing about the programming logic in the script. There may be all kind of error handling going on - or none at all. I don't know, if the mentioned URLs are vulnerable. I'm not going to test it :-)